Key tactics of origin-based user equilibrium (OUE) algorithm was studied,which involved the algorithm procedure and several implementation issues.To speed up the convergence,update policies of flows,costs and bushes w...Key tactics of origin-based user equilibrium (OUE) algorithm was studied,which involved the algorithm procedure and several implementation issues.To speed up the convergence,update policies of flows,costs and bushes were proposed.The methods of step-size searching and bush construction are proved to be practical.The modified OUE algorithm procedure was also optimized to take the advantage of multi-thread process.Convergence performances were compared with those of other algorithms by different sizes of urban transportation networks.The result shows this modified OUE algorithm is more efficient and consumes less time to achieve the reasonable relative gap in practical applications.展开更多
This paper presents a hybrid symbolic-numeric algorithm to compute ranking functions for establishing the termination of loop programs with polynomial guards and polynomial assignments.The authors first transform the ...This paper presents a hybrid symbolic-numeric algorithm to compute ranking functions for establishing the termination of loop programs with polynomial guards and polynomial assignments.The authors first transform the problem into a parameterized polynomial optimization problem,and obtain a numerical ranking function using polynomial sum-of-squares relaxation via semidefinite programming(SDP).A rational vector recovery algorithm is deployed to recover a rational polynomial from the numerical ranking function,and some symbolic computation techniques are used to certify that this polynomial is an exact ranking function of the loop programs.At last,the authors demonstrate on some polynomial loop programs from the literature that our algorithm successfully yields nonlinear ranking functions with rational coefficients.展开更多
In this study, we propose and compare stochastic variants of the extra-gradient alternating direction method, named the stochastic extra-gradient alternating direction method with Lagrangian function（SEGL） and the s...In this study, we propose and compare stochastic variants of the extra-gradient alternating direction method, named the stochastic extra-gradient alternating direction method with Lagrangian function（SEGL） and the stochastic extra-gradient alternating direction method with augmented Lagrangian function（SEGAL）, to minimize the graph-guided optimization problems, which are composited with two convex objective functions in large scale.A number of important applications in machine learning follow the graph-guided optimization formulation, such as linear regression, logistic regression, Lasso, structured extensions of Lasso, and structured regularized logistic regression. We conduct experiments on fused logistic regression and graph-guided regularized regression. Experimental results on several genres of datasets demonstrate that the proposed algorithm outperforms other competing algorithms, and SEGAL has better performance than SEGL in practical use.展开更多
基金Projects(70631002,70701027) supported by the National Natural Science Foundation of ChinaProject(NCET-08-0406) supported by the Program for New Century Excellent Talents in Chinese University
文摘Key tactics of origin-based user equilibrium (OUE) algorithm was studied,which involved the algorithm procedure and several implementation issues.To speed up the convergence,update policies of flows,costs and bushes were proposed.The methods of step-size searching and bush construction are proved to be practical.The modified OUE algorithm procedure was also optimized to take the advantage of multi-thread process.Convergence performances were compared with those of other algorithms by different sizes of urban transportation networks.The result shows this modified OUE algorithm is more efficient and consumes less time to achieve the reasonable relative gap in practical applications.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.10901055,61021004,91118007by NKBRPC 2011CB302802,2011CB70690by the Fundamental Research Funds for the Central Universities under Grant No.78210043
文摘This paper presents a hybrid symbolic-numeric algorithm to compute ranking functions for establishing the termination of loop programs with polynomial guards and polynomial assignments.The authors first transform the problem into a parameterized polynomial optimization problem,and obtain a numerical ranking function using polynomial sum-of-squares relaxation via semidefinite programming(SDP).A rational vector recovery algorithm is deployed to recover a rational polynomial from the numerical ranking function,and some symbolic computation techniques are used to certify that this polynomial is an exact ranking function of the loop programs.At last,the authors demonstrate on some polynomial loop programs from the literature that our algorithm successfully yields nonlinear ranking functions with rational coefficients.
基金supported by the National Natural Science Foundation of China(No.61303264)the National Key Research and Development Program of China(No.2016YFB1000401)
文摘In this study, we propose and compare stochastic variants of the extra-gradient alternating direction method, named the stochastic extra-gradient alternating direction method with Lagrangian function（SEGL） and the stochastic extra-gradient alternating direction method with augmented Lagrangian function（SEGAL）, to minimize the graph-guided optimization problems, which are composited with two convex objective functions in large scale.A number of important applications in machine learning follow the graph-guided optimization formulation, such as linear regression, logistic regression, Lasso, structured extensions of Lasso, and structured regularized logistic regression. We conduct experiments on fused logistic regression and graph-guided regularized regression. Experimental results on several genres of datasets demonstrate that the proposed algorithm outperforms other competing algorithms, and SEGAL has better performance than SEGL in practical use.
